Introduction
-
The proposed VSMPSO, does not focus on improving the accuracy of surrogate models, but rather relies on the blessing of uncertainty [36], which only employs one RBF model as a single surrogate in combination with the proposed variable surrogate model strategy to explore different promising area in different generation to avoid model misdirection throughout the whole optimization process.
-
The prediction ability of the surrogate model is not only used to predict the current population. For deep mining of the surrogate model prediction information, the most promising point of the surrogate model would be found and transferred into the optimizer population to accelerate the optimization.
-
The proposed algorithm framework of VSMPSO can be applied in any surrogate-assisted evolutionary algorithm irrespective of the surrogate model used.
Related techniques in VSMPSO
Particle swarm optimization (PSO)
RBF network
Proposed VSMPSO algorithm
VSMPSO framework
Variable model management strategy
Knowledge transfer strategy
Function | No. of variables | Global optimum |
---|---|---|
F1: Ellipsoid | 30/50/100/200 | 0 |
F2: Rosenbrock | 0 | |
F3: Ackley | 0 | |
F4: Griewank | 0 | |
F5: Rastrigin | 0 | |
F6: Shifted rotated Rastrigin function (F10 in [47]) | \(-\) 300 | |
F7: Rotated hybrid composition function (F19 in [47]) | 10 | |
F8: Shifted rotated Rastrigin function (F25 in [48]) | 50/100 | 2500 |
F9: Rotated hybrid composition function (F26 in [48]) | 2600 | |
F10: Rotated hybrid composition function (F27 in [48]) | 2700 | |
F11: Rotated hybrid composition function (F28 in [48]) | 2800 |
Function | Algorithm | Best | Worst | Mean (Friedman test) | SD |
---|---|---|---|---|---|
F1: Ellipsoid | VSMPSO(GP) | 7.88E\(-\)06 | 1.68E\(-\)05 | 1.34E\(-\)05 | 2.17E\(-\)06 |
VSMPSO(RBF) | 2.67E\(-\)01 | 9.20E+00 | 2.33E+00 | 1.81E+00 | |
MGP-SLPSO |
2.31E
\(-\)
11
|
1.41E
\(-\)
10
| 7.22E \(-\)11(+) |
3.05E
\(-\)
11
| |
CAL-SAPSO | 2.64E\(-\)01 | 1.14E+01 | 2.69E+00 | 2.68E+00 | |
SAHO | 1.33E\(-\)02 | 4.15E\(-\)01 | 1.39E\(-\)01 | 1.03E\(-\)01 | |
SACOSO | 1.59E+02 | 4.98E+02 | 2.98E+02 | 8.36E+01 | |
F2: Rosenbrock | VSMPSO(GP) | 5.53E+01 | 7.62E+01 | 7.40E+01 | 6.59E+00 |
VSMPSO(RBF) | 1.03E+02 | 2.13E+02 | 1.52E+02 | 2.80E+01 | |
MGP-SLPSO | 7.28E+01 | 2.87E+02 | 1.20E+02 | 3.91E+01 | |
CAL-SAPSO | 3.51E+01 | 9.64E+01 | 5.34E+01 |
1.29E+01
| |
SAHO |
2.93E+01
|
9.58E+01
| 3.30E+01(+) | 2.09E+01 | |
SACOSO | 2.71E+02 | 1.09E+03 | 5.80E+02 | 2.00E+02 | |
F3: Ackley | VSMPSO(GP) | 4.16E+00 | 1.34E+01 | 1.19E+01 | 3.36E+00 |
VSMPSO(RBF) | 3.43E+00 | 5.15E+00 | 4.03E+00 |
4.68E
\(-\)
01
| |
MGP-SLPSO | 5.53E+00 | 1.77E+01 | 1.02E+01 | 3.10E+00 | |
CAL-SAPSO | 8.00E+00 | 1.96E+01 | 1.44E+01 | 3.31E+00 | |
SAHO |
6.54E
\(-\)
02
|
2.54E+00
| 1.92E+00(+) | 5.83E\(-\)01 | |
SACOSO | 1.09E+01 | 1.65E+01 | 1.30E+01 | 1.36E+00 | |
F4: Griewank | VSMPSO(GP) |
2.15E
\(-\)
03
|
3.35E
\(-\)
03
| 2.39E \(-\)03(+) |
4.99E
\(-\)
04
|
VSMPSO(RBF) | 6.50E\(-\)01 | 1.00E+00 | 8.54E\(-\)01 | 8.07E\(-\)02 | |
MGP-SLPSO | 6.70E\(-\)03 | 3.44E\(-\)02 | 1.43E\(-\)02 | 6.20E\(-\)03 | |
CAL-SAPSO | 1.22E+00 | 1.88E+00 | 1.49E+00 | 1.49E\(-\)01 | |
SAHO | 1.01E\(-\)02 | 4.55E\(-\)01 | 1.40E\(-\)01 | 1.12E\(-\)01 | |
SACOSO | 3.74E+01 | 8.99E+01 | 5.83E+01 | 1.37E+01 | |
F5: Rastrigin | VSMPSO(GP) | 2.12E+02 | 2.64E+02 | 2.36E+02 | 2.02E+01 |
VSMPSO(RBF) | 2.01E+02 | 2.94E+02 | 2.51E+02 | 2.42E+01 | |
MGP-SLPSO | 2.90E+01 | 1.46E+02 | 8.02E+01 | 2.82E+01 | |
CAL-SAPSO | 1.97E+01 |
5.84E+01
| 3.58E+01(+) |
1.20E+01
| |
SAHO |
5.04E+00
| 1.12E+02 | 4.66E+01 | 2.70E+01 | |
SACOSO | 2.35E+02 | 3.34E+02 | 2.90E+02 | 2.21E+01 | |
F6 (F10 in CEC05) | VSMPSO(GP) | \(-\) 8.58E+01 | \(-\) 5.25E+01 | \(-\) 7.43E+01 | 1.27E+01 |
VSMPSO(RBF) | \(-\) 8.90E+01 | 1.26E+01 | \(-\) 4.76E+01 | 2.54E+01 | |
MGP-SLPSO | \(-\) 2.12E+02 | \(-\) 5.39E+01 | \(-\) 1.46E+02 | 3.41E+01 | |
CAL-SAPSO | 2.49E\(-\)01 | 2.20E+00 | 1.32E+00 |
5.83E
\(-\)
01
| |
SAHO | \(-\) 2.68E+02 | \(-\) 1.21E+02 | \(-\) 2.11E+02(+) | 3.34E+01 | |
SACOSO | \(-\) 4.51E+00 | 1.45E+02 | 8.67E+01 | 3.77E+01 | |
F7 (F19 in CEC05) | VSMPSO(GP) | 9.40E+02 |
9.56E+02
| 9.48E+02(\(\approx \)) |
6.13E+00
|
VSMPSO(RBF) |
9.26E+02
| 9.97E+02 | 9.43E+02(+) | 1.51E+01 | |
MGP-SLPSO | 1.01E+03 | 1.18E+03 | 1.10E+03 | 3.65E+01 | |
CAL-SAPSO | 1.06E+03 | 1.34E+03 | 1.18E+03 | 5.54E+01 | |
SAHO | 9.29E+02 | 1.10E+03 | 9.67E+02 | 3.60E+01 | |
SACOSO | 1.07E+03 | 1.28E+03 | 1.17E+03 | 5.07E+01 |
Experimental studies
Fuction | VSMPSO(GP) | VSMPSO(RBF) | MGP-SLPSO | CAL-SAPSO | SAHO | SACOSO |
---|---|---|---|---|---|---|
30D/330FEs | Best fitness/time | Best fitness/time | Best fitness/time | Best fitness/time | Best fitness/time | Best fitness/time |
F1: Ellipsoid | 1.34E \(-\) 05/2.37E + 01 | 2.33E + 00/5.45E + 01 | 7.22E\(-\)11/1.45E + 01 | 2.69E + 00/3.97E + 03 | 1.39E \(-\) 01/3.60E + 03 | 2.98E + 02/6.07E + 01 |
F2: Rosenbrock | 7.40E + 01/2.93E + 01 | 1.52E + 02/6.86E + 00 | 1.20E + 02/8.15E + 01 | 5.34E + 01/4.04E + 03 | 3.30E + 01/3.95E + 03 | 5.80E + 02/6.86E + 01 |
F3: Ackley | 1.19E + 01/5.34E + 01 | 4.03E + 00/5.52E + 01 | 1.02E + 01/4.63E + 01 | 1.44E + 01/3.88E + 03 | 1.92E + 00/4.15E + 03 | 1.30E + 01/7.00E + 01 |
F4: Griewank | 2.39E \(-\) 03/2.47E + 01 | 8.54E \(-\) 01/5.64E + 01 | 1.43E \(-\) 02/1.43E + 01 | 1.49E + 00/3.87E + 03 | 1.40E \(-\) 01/3.99E + 03 | 5.83E + 01/8.43E + 01 |
F5: Rastrigin | 2.36E + 02/1.08E + 03 | 2.51E + 02/5.52E + 01 | 8.02E + 01/8.79E + 01 | 3.58E + 01/3.80E + 03 | 4.66E + 01/4.53E + 03 | 2.90E + 02/6.48E + 01 |
F6 (F10 in CEC05) | \(-\) 7.43E + 01/4.02E+02 | \(-\) 4.76E + 01/5.55E + 01 | \(-\) 1.46E + 02/1.72E + 02 | 1.32E + 00/8.95E + 03 | \(-\) 2.11E + 02/1.97E + 03 | 8.67E + 01/8.08E + 01 |
F7 (F19 in CEC05) | 9.48E + 02/6.29E + 02 | 9.43E + 02/5.58E + 01 | 1.10E + 03/5.84E + 01 | 1.18E + 03/8.93E + 03 | 9.67E + 02/2.32E + 03 | 1.17E + 03/9.88E + 01 |
All/NDS/DS | 7/2/5. | 7/5/2 | 7/5/2 | 7/1/6 | 7/4/3 | 7/0/7 |
Fuction | VSMPSO(GP) | VSMPSO(RBF) | MGP-SLPSO | SAHO | SACOSO |
---|---|---|---|---|---|
F1: Ellipsoid | 9.80E+00/7.98E+03 | 1.19E+01/1.72E+02 | 8.53E\(-\)05/1.97E+01 | 1.22E\(-\)01/3.39E+03 | 4.93E+01/1.18E+03 |
F2: Rosenbrock | 2.50E+02/1.19E+04 | 1.88E+02/1.61E+02 | 1.83E+02/9.86E+01 | 4.85E+01/1.25E+04 | 2.49E+02/1.15E+03 |
F3: Ackley | 6.90E+00/1.55E+04 | 8.68E+00/1.81E+02 | 1.43E+01/9.01E+01 | 5.39E\(-\)02/4.86E+03 | 1.30E+01/2.05E+02 |
F4: Griewank | 2.63E+00/7.70E+03 | 8.34E\(-\)01/1.80E+02 | 1.80E\(-\)03/2.11E+01 | 6.21E\(-\)01/3.72E+03 | 5.54E+00/1.36E+03 |
F5: Rastrigin | 4.18E+02/1.50E+04 | 4.04E+02/1.74E+02 | 2.95E+02/2.17E+02 | 1.52E+02/6.27E+03 | 4.24E+02/2.54E+02 |
F6 (F10 in CEC05) | 9.08E+01/8.00E+03 | 1.05E+02/1.76E+02 | 1.18E+02/6.42E+02 | 8.19E+01/7.69E+03 | 2.14E+02/1.10E+03 |
F7 (F19 in CEC05) | 1.06E+03/1.37E+04 | 9.81E+02/1.77E+02 | 1.10E+03/2.16E+03 | 9.73E+02/6.33E+03 | 1.08E+03/1.34E+03 |
All/NDS/DS | 7/0/7 | 7/4/3 | 7/5/2 | 7/5/2 | 7/0/7 |
Experimental setup in details
Numerical results on 30- and 50-D F1–F7 functions
Numerical results and analysis on 50D F1–F7 functions with 2000 FEs
Function | Algorithm | Best | Worst | Mean (Friedman test) | SD |
---|---|---|---|---|---|
F1: Ellipsoid | VSMPSO(GP) | 7.09E+00 | 1.10E+01 | 9.80E+00 | 1.40E+00 |
VSMPSO(RBF) | 3.79E+00 | 2.53E+01 | 1.19E+01 | 6.13E+00 | |
MGP-SLPSO | 9.31E \(-\)06 | 1.80E \(-\)03 | 8.53E \(-\)05(+) | 3.23E \(-\)04 | |
SAHO | 1.38E\(-\)02 | 6.59E\(-\)01 | 1.22E\(-\)01 | 1.51E\(-\)01 | |
SACOSO | 2.38E+01 | 8.38E+01 | 4.93E+01 | 1.60E+01 | |
F2: Rosenbrock | VSMPSO(GP) | 4.07E+02 | 7.36E+02 | 2.50E+02 | 1.33E+02 |
VSMPSO(RBF) | 1.14E+02 | 2.75E+02 | 1.88E+02 | 3.04E+01 | |
MGP-SLPSO | 1.37E+02 | 2.48E+02 | 1.83E+02 | 2.79E+01 | |
SAHO | 4.82E+01 | 4.87E+01 | 4.85E+01(+) | 1.22E \(-\)01 | |
SACOSO | 1.54E+02 | 3.64E+02 | 2.49E+02 | 5.43E+01 | |
F3: Ackley | VSMPSO(GP) | 6.52E+00 | 7.38E+00 | 6.90E+00 | 4.21E\(-\)01 |
VSMPSO(RBF) | 4.09E+00 | 2.00E+01 | 8.68E+00 | 6.36E+00 | |
MGP-SLPSO | 1.15E+01 | 1.57E+01 | 1.43E+01 | 1.31E+00 | |
SAHO | 2.38E \(-\)02 | 1.64E \(-\)01 | 5.39E \(-\)02(+) | 2.97E \(-\)02 | |
SACOSO | 1.06E+01 | 1.46E+01 | 1.30E+01 | 1.00E+00 | |
F4: Griewank | VSMPSO(GP) | 2.37E+00 | 3.15E+00 | 2.63E+00 | 3.09E\(-\)01 |
VSMPSO(RBF) | 6.42E\(-\)01 | 9.84E\(-\)01 | 8.34E\(-\)01 | 7.38E\(-\)02 | |
MGP-SLPSO | 9.51E \(-\)04 | 4.20E \(-\)03 | 1.80E \(-\)03(+) | 6.79E \(-\)04 | |
SAHO | 2.80E\(-\)01 | 9.02E\(-\)01 | 6.21E\(-\)01 | 1.37E\(-\)01 | |
SACOSO | 3.69E+00 | 7.61E+00 | 5.54E+00 | 1.04E+00 | |
F5: Rastrigin | VSMPSO(GP) | 4.14E+02 | 4.34E+02 | 4.18E+02 | 6.86E+00 |
VSMPSO(RBF) | 2.50E+02 | 4.81E+02 | 4.04E+02 | 5.97E+01 | |
MGP-SLPSO | 2.05E+02 | 4.29E+02 | 2.95E+02 | 5.78E+01 | |
SAHO | 5.31E+01 | 4.05E+02 | 1.52E+02(+) | 8.04E+01 | |
SACOSO | 3.58E+02 | 4.74E+02 | 4.24E+02 | 2.99E+01 | |
F6 (F10 in CEC05) | VSMPSO(GP) | 7.80E+01 | 1.21E+02 | 9.08E+01 | 1.21E+01 |
VSMPSO(RBF) | \(-\) 1.15E+01 | 1.87E+02 | 1.05E+02 | 5.72E+01 | |
MGP-SLPSO | 3.35E+01 | 1.75E+02 | 1.18E+02 | 3.74E+01 | |
SAHO | \(-\) 1.19E+02 | 3.51E+02 | 8.19E+01(+) | 1.13E+02 | |
SACOSO | 1.48E+02 | 2.95E+02 | 2.14E+02 | 3.33E+01 | |
F7 (F19 in CEC05) | VSMPSO(GP) | 1.02E+03 | 1.10E+03 | 1.06E+03 | 3.46E+01 |
VSMPSO(RBF) | 9.49E+02 | 1.04E+03 | 9.81E+02 (\(\approx \)) | 2.49E+01 | |
MGP-SLPSO | 1.02E+03 | 1.17E+03 | 1.10E+03 | 4.15E+01 | |
SAHO | 9.53E+02 | 1.03E+03 | 9.73E+02(+) | 1.91E+01 | |
SACOSO | 1.00E+03 | 1.16E+03 | 1.08E+03 | 3.66E+01 |
Function | Algorithm | Best | Worst | Mean (Friedman test) | SD |
---|---|---|---|---|---|
F1: Ellipsoid | VSMPSO | 4.01E\(-\)02 | 7.60E\(-\)02 | 5.05E\(-\)02 | 1.05E\(-\)02 |
MGP-SLPSO |
4.72E
\(-\)
26
|
1.90E
\(-\)
24
| 2.47E \(-\)25(+) |
5.82E
\(-\)
25
| |
SAHO | 6.75E\(-\)16 | 4.41E\(-\)07 | 3.49E\(-\)10 | 9.94E\(-\)08 | |
SACOSO | 1.36E+00 | 6.90E+00 | 3.98E+00 | 1.45E+00 | |
F2: Rosenbrock | VSMPSO | 5.92E+01 | 1.18E+02 | 8.30E+01 | 2.47E+01 |
MGP-SLPSO | 1.78E+02 | 2.19E+02 | 1.95E+02 | 1.40E+01 | |
SAHO |
4.56E+01
|
4.63E+01
| 4.61E+01(+) |
1.42E
\(-\)
01
| |
SACOSO | 5.41E+01 | 1.85E+02 | 9.01E+01 | 3.24E+01 | |
F3: Ackley | VSMPSO | 3.18E+00 | 5.38E+00 | 4.09E+00 | 7.89E\(-\)01 |
MGP-SLPSO | 9.44E+02 | 9.86E+02 | 9.60E+02 | 1.18E+01 | |
SAHO |
1.29E
\(-\)
12
|
2.14E
\(-\)
11
| 4.49E \(-\)12(+) |
4.72E
\(-\)
12
| |
SACOSO | 1.06E+01 | 1.46E+01 | 1.30E+01 | 1.00E+00 | |
F4: Griewank | VSMPSO | 2.71E\(-\)04 | 1.80E\(-\)03 | 7.50E\(-\)04 | 7.00E\(-\)04 |
MGP-SLPSO | 5.57E\(-\)09 |
8.65E
\(-\)
05
| 2.19E\(-\)05 |
3.61E
\(-\)
05
| |
SAHO |
1.30E
\(-\)
11
| 1.24E\(-\)02 | 3.73E \(-\)10(+) | 2.84E\(-\)03 | |
SACOSO | 3.69E+00 | 7.61E+00 | 5.54E+00 | 1.04E+00 | |
F5: Rastrigin | VSMPSO |
8.76E+01
|
1.45E+02
| 1.04E+02(+) |
1.60E+01
|
MGP-SLPSO | 1.91E+02 | 4.15E+02 | 2.72E+02 | 7.33E+01 | |
SAHO | 4.88E+01 | 1.63E+02 | 1.06E+02 | 2.80E+01 | |
SACOSO | 9.11E+01 | 2.72E+02 | 1.73E+02 | 3.81E+01 | |
F6 (F10 in CEC05) | VSMPSO | \(-\) 2.28E+02 | \(-\) 1.79E+02 | \(-\) 1.94E+02(+) |
1.39E+01
|
MGP-SLPSO | 5.80E+01 | 1.37E+02 | 1.05E+02 | 2.85E+01 | |
SAHO | \(-\) 2.25E+02 | \(-\) 1.84E+01 | \(-\) 1.29E+02 | 4.95E+01 | |
SACOSO | \(-\) 2.58E+01 | 2.51E+02 | 1.54E+02 | 4.97E+01 | |
F7 (F19 in CEC05) | VSMPSO | 9.44E+02 |
9.86E+02
| 9.60E+02(\(\approx \)) |
1.18E+01
|
MGP-SLPSO | 1.08E+03 | 1.19E+03 | 1.14E+03 | 3.38E+01 | |
SAHO |
9.39E+02
| 1.03E+03 | 9.51E+02(+) | 2.12E+01 | |
SACOSO | 9.81E+02 | 1.12E+03 | 1.03E+03 | 3.22E+01 |
Mean/time | VSMPSO | MGP-SLPSO | SAHO | SACOSO |
---|---|---|---|---|
F1: Ellipsoid | 5.05E\(-\)02/3.14E+03 | 2.47E\(-\)25/1.82E+02 | 3.49E\(-\)10/1.13E+04 | 3.98E+00/1.25E+03 |
F2: Rosenbrock | 8.30E+01/3.14E+03 | 1.95E+02/6.34E+02 | 4.61E+01/1.16E+04 | 9.01E+01/1.24E+03 |
F3: Ackley | 4.09E+00/3.15E+03 | 9.60E+02/3.44E+02 | 4.49E\(-\)12/1.06E+04 | 1.30E+01/2.05E+02 |
F4: Griewank | 7.50E\(-\)04/3.14E+03 | 2.19E\(-\)05/2.03E+02 | 3.73E\(-\)10/1.14E+04 | 5.54E+00/1.36E+03 |
F5: Rastrigin | 1.04E+02/3.15E+03 | 1.04E+02/6.02E+02 | 1.06E+02/2.37E+04 | 1.73E+02/1.29E+03 |
F6 (F10 in CEC05) | \(-\) 1.94E+02/3.98E+03 | 1.05E+02/2.45E+03 | 1.29E+02/1.86E+04 | 1.54E+02/1.25E+03 |
F7 (F19 in CEC05) | 9.60E+02/4.01E+03 | 1.14E+03/1.19E+03 | 9.51E+02/2.77E+04 | 1.03E+03/1.31E+03 |
All/NDS/DS | 7/5/2 |
7/7/0
| 7/4/3 | 7/5/2 |
Numerical results on higher dimensional problems
Function | Algorithm | Best | Worst | Mean (Friedman test) | SD |
---|---|---|---|---|---|
F1: Ellipsoid | VSMPSO | 2.17E+01 | 6.20E+01 | 3.60E+01 | 9.31E+00 |
MGP-SLPSO | 4.37E \(-\)17 | 3.17E \(-\)02 | 1.10E \(-\)03(+) | 5.80E \(-\)03 | |
SAHO | 2.80E\(-\)02 | 1.99E+00 | 5.02E\(-\)02 | 3.55E\(-\)01 | |
SACOSO | 5.94E+02 | 1.39E+03 | 9.29E+02 | 2.36E+02 | |
F2: Rosenbrock | VSMPSO | 1.53E+02 | 2.40E+02 | 1.88E+02 | 2.07E+01 |
MGP-SLPSO | 4.58E+02 | 8.59E+02 | 6.28E+02 | 1.05E+02 | |
SAHO | 9.78E+01 | 9.82E+01 | 9.80E+01(+) | 7.37E \(-\)02 | |
SACOSO | 1.46E+03 | 4.64E+03 | 2.41E+03 | 7.99E+02 | |
F3: Ackley | VSMPSO | 8.24E+00 | 1.25E+01 | 1.06E+01 | 8.99E\(-\)01 |
MGP-SLPSO | 1.71E+01 | 1.85E+01 | 1.80E+01 | 3.47E\(-\)01 | |
SAHO | 9.60E \(-\)03 | 2.94E \(-\)02 | 1.48E \(-\)02(+) | 4.84E \(-\)03 | |
SACOSO | 1.42E+01 | 1.72E+01 | 1.59E+01 | 7.44E\(-\)01 | |
F4: Griewank | VSMPSO | 6.58E\(-\)01 | 1.01E+00 | 8.17E\(-\)01 | 8.24E\(-\)02 |
MGP-SLPSO | 3.10E \(-\)02 | 1.31E \(-\)01 | 7.37E \(-\)02(+) | 2.51E \(-\)02 | |
SAHO | 1.02E\(-\)01 | 6.52E\(-\)01 | 2.51E\(-\)01 | 1.54E\(-\)01 | |
SACOSO | 4.14E+01 | 1.06E+02 | 6.90E+01 | 1.50E+01 | |
F5: Rastrigin | VSMPSO | 3.09E+02 | 7.32E+02 | 4.79E+02 | 8.71E+01 |
MGP-SLPSO | 1.09E+03 | 1.24E+03 | 1.18E+03 | 3.52E+01 | |
SAHO | 1.23E+02 | 3.85E+02 | 2.54E+02(+) | 6.01E+01 | |
SACOSO | 7.84E+02 | 9.63E+02 | 8.65E+02 | 4.87E+01 | |
F6 (F10 in CEC05) | VSMPSO | 5.86E+02 | 8.36E+02 | 7.28E+02(+) | 6.55E+01 |
MGP-SLPSO | 7.79E+02 | 1.38E+03 | 9.77E+02 | 1.09E+02 | |
SAHO | 7.39E+02 | 1.17E+03 | 9.44E+02 | 9.05E+01 | |
SACOSO | 1.10E+03 | 1.60E+03 | 1.34E+03 | 1.13E+02 | |
F7 (F19 in CEC05) | VSMPSO | 1.33E+03 | 1.46E+03 | 1.40E+03 (\(\approx \)) | 4.05E+01 |
MGP-SLPSO | 1.35E+03 | 1.54E+03 | 1.41E+03 (\(\approx \)) | 4.12E+01 | |
SAHO | 9.10E+02 | 1.42E+03 | 1.38E+03(+) | 1.22E+02 | |
SACOSO | 1.35E+03 | 1.52E+03 | 1.41E+03 (\(\approx \)) | 3.80E+01 |
Mean/time | VSMPSO | MGP-SLPSO | SAHO | SACOSO |
---|---|---|---|---|
Ellipsoid | 3.60E+01/8.71E+02 | 1.10E\(-\)03/5.17E+02 | 5.02E\(-\)02/1.48E+04 | 1.10E\(-\)03/5.17E+02 |
Rosenbrock | 1.88E+02/6.07E+02 | 6.28E+02/2.62E+03 | 9.80E+01/1.49E+04 | 6.28E+02/2.62E+03 |
Ackley | 1.06E+01/8.33E+02 | 1.80E+01/2.20E+03 | 1.48E\(-\)02/1.44E+04 | 1.80E+01/2.20E+03 |
Griewank | 8.17E\(-\)01/8.49E+02 | 7.37E\(-\)02/5.21E+02 | 2.51E\(-\)01/1.47E+04 | 7.37E\(-\)02/5.21E+02 |
Rastrigin | 4.79E+02/8.80E+02 | 1.18E+03/4.01E\(-\)02 | 2.54E+02/5.16E+04 | 8.65E+02/7.76E+02 |
F6 (F10 in CEC05) | 7.28E+02/9.45E+02 | 9.77E+02/2.93E+03 | 9.44E+02/2.59E+04 | 9.77E+02/2.93E+03 |
F7 (F19 in CEC05) | 1.40E+03/1.11E+03 | 1.41E+03/8.30E+03 | 1.38E+03/3.87E+04 | 1.41E+03/8.30E+03 |
All/NDS/DS |
7/5/2
| 7/3/4 | 7/4/3 | 7/1/6 |
Function | Algorithm | Best | Worst | Mean | SD |
---|---|---|---|---|---|
F1: Ellipsoid | VSMPSO | 1.63E+02 | 2.99E+02 | 2.25E+02 | 3.48E+01 |
MGP-SLPSO |
2.51E
\(-\)
04
|
1.21E
\(-\)
02
| 6.80E \(-\)03(+) |
3.10E
\(-\)
03
| |
SACOSO | 6.07E+03 | 1.47E+04 | 9.27E+03 | 2.12E+03 | |
F2: Rosenbrock | VSMPSO |
2.68E+02
|
3.20E+02
| 2.94E+02(+) |
1.45E+01
|
MGP-SLPSO | 7.96E+03 | 1.20E+04 | 1.06E+04 | 1.62E+03 | |
SACOSO | 4.22E+03 | 1.76E+04 | 9.52E+03 | 3.06E+03 | |
F3: Ackley | VSMPSO |
1.21E+01
|
1.42E+01
| 1.33E+01(+) | 5.48E\(-\)01 |
MGP-SLPSO | 1.47E+03 | 1.52E+03 | 1.49E+03 | 1.28E+01 | |
SACOSO | 2.05E+01 | 2.09E+01 | 2.07E+01 |
1.01E
\(-\)
01
| |
F4: Griewank | VSMPSO | 1.01E+00 | 1.18E+00 | 1.09E+00 |
3.96E
\(-\)
02
|
MGP-SLPSO |
4.91E
\(-\)
05
|
1.09E+00
| 1.57E \(-\)01(+) | 3.30E\(-\)01 | |
SACOSO | 2.19E+02 | 5.01E+02 | 3.33E+02 | 7.54E+01 | |
F5: Rastrigin | VSMPSO |
8.64E+02
|
1.35E+03
| 1.07E+03(+) | 1.35E+02 |
MGP-SLPSO | 2.15E+03 | 2.37E+03 | 2.23E+03 | 8.41E+01 | |
SACOSO | 1.68E+03 | 2.12E+03 | 1.87E+03 |
7.42E+01
| |
F6 (F10 in CEC05) | VSMPSO | 5.10E+03 | 5.92E+03 | 5.65E+03 | 1.98E+02 |
MGP-SLPSO |
5.06E+03
|
5.76E+03
| 5.49E+03 | 1.93E+02 | |
SACOSO | 5.12E+03 | 5.65E+03 | 5.45E+03(+) |
1.30E+02
| |
F7 (F19 in CEC05) | VSMPSO | 1.47E+03 | 1.52E+03 | 1.49E+03 | 1.28E+01 |
MGP-SLPSO | 1.44E+03 |
1.46E+03
| 1.45E+03(+) |
1.17E+01
| |
SACOSO |
1.41E+03
| 1.49E+03 | 1.46E+03(\(\approx \)) | 1.67E+01 |
Function | VSMPSO | MGP-SLPSO | SACOSO |
---|---|---|---|
F1: Ellipsoid | 2.25E+02/9.73E+03 | 6.80E\(-\)03/1.34E+03 | 9.27E+03/9.29E+03 |
F2: Rosenbrock | 2.94E+02/9.62E+03 | 1.06E+04/1.57E+03 | 9.52E+03/9.48E+03 |
F3: Ackley | 1.33E+01/9.69E+03 | 1.49E+03/3.12E+03 | 2.07E+01/7.14E+03 |
F4: Griewank | 1.09E+00/9.72E+03 | 1.57E\(-\)01/1.62E+03 | 3.33E+02/9.88E+03 |
F5: Rastrigin | 1.07E+03/9.90E+03 | 2.23E+03/1.85E+03 | 1.87E+03/3.82E+03 |
F6 (F10 in CEC05) | 5.65E+03/5.70E+03 | 5.49E+03/9.25E+03 | 5.45E+03/1.07E+04 |
F7 (F19 in CEC05) | 1.49E+03/7.31E+03 | 1.45E+03/5.94E+03 | 1.46E+03/1.11E+04 |
All/NDS/DS | 7/4/3 | 7/7/0 | 7/3/4 |
Effects of variable model management strategy
Function | Algorithm | Best | Worst | Mean (Friedman test) | SD |
---|---|---|---|---|---|
F1: Ellipsoid | SMPSO-RS | 1.67E+00 | 3.42E+01 | 8.84E+00 | 7.73E+00 |
SMPSO-AS | 3.54E\(-\)01 | 1.55E+01 | 4.21E+00 | 3.53E+00 | |
SMPSO-FS1 | 8.51E+00 | 1.22E+02 | 4.77E+01 | 3.16E+01 | |
SMPSO-FS2 | 1.14E+01 | 9.31E+01 | 3.68E+01 | 2.17E+01 | |
VSMPSO | 2.67E \(-\)01 | 9.20E+00 | 2.33E+00(+) | 1.81E+00 | |
F2: Rosenbrock | SMPSO-RS | 1.03E+02 | 2.13E+02 | 1.52E+02 | 2.80E+01 |
SMPSO-AS | 8.35E+01 | 1.92E+02 | 1.38E+02 | 3.05E+01 | |
SMPSO-FS1 | 1.54E+02 | 9.40E+02 | 3.01E+02 | 1.79E+02 | |
SMPSO-FS2 | 1.53E+02 | 5.69E+02 | 2.62E+02 | 9.14E+01 | |
VSMPSO | 5.99E+01 | 2.03E+02 | 1.12E+02(+) | 3.01E+01 | |
F3: Ackley | SMPSO-RS | 3.21E+00 | 1.52E+01 | 5.43E+00 | 2.45E+00 |
SMPSO-AS | 3.40E+00 | 1.16E+01 | 6.07E+00 | 2.13E+00 | |
SMPSO-FS1 | 9.57E+00 | 1.90E+01 | 1.49E+01 | 2.77E+00 | |
SMPSO-FS2 | 8.30E+00 | 2.00E+01 | 1.51E+01 | 2.77E+00 | |
VSMPSO | 3.43E+00 | 5.15E+00 | 4.03E+00(+) | 4.68E \(-\)01 | |
F4: Griewank | SMPSO-RS | 4.77E\(-\)01 | 1.06E+00 | 7.98E\(-\)01 | 1.68E \(-\)01 |
SMPSO-AS | 1.59E \(-\)01 | 8.17E \(-\)01 | 4.98E \(-\)01(+) | 1.87E\(-\)01 | |
SMPSO-FS1 | 1.36E+00 | 6.22E+00 | 3.26E+00 | 1.14E+00 | |
SMPSO-FS2 | 1.71E+00 | 5.56E+00 | 3.33E+00 | 9.85E\(-\)01 | |
VSMPSO | 6.50E\(-\)01 | 1.00E+00 | 8.54E\(-\)01 | 8.07E\(-\)02 | |
F5: Rastrigin | SMPSO-RS | 3.72E+01 | 1.62E+02 | 9.92E+01 | 2.80E+01 |
SMPSO-AS | 5.01E+01 | 1.23E+02 | 8.80E+01(+) | 1.69E+01 | |
SMPSO-FS1 | 1.96E+02 | 3.22E+02 | 2.64E+02 | 2.96E+01 | |
SMPSO-FS2 | 2.22E+02 | 3.50E+02 | 2.95E+02 | 3.38E+01 | |
VSMPSO | 2.01E+02 | 2.94E+02 | 2.51E+02 | 2.42E+01 | |
F6 (F10 in CEC05) | SMPSO-RS | \(-\) 2.70E+02 | \(-\) 8.34E+01 | \(-\) 2.09E+02 | 3.68E+01 |
SMPSO-AS | \(-\) 2.71E+02 | \(-\) 1.69E+02 | \(-\) 2.18E+02(+) | 2.90E+01 | |
SMPSO-FS1 | \(-\) 1.23E+01 | 1.24E+02 | 6.03E+01 | 3.61E+01 | |
SMPSO-FS2 | \(-\) 6.45E+01 | 1.37E+02 | 4.99E+01 | 4.97E+01 | |
VSMPSO | \(-\) 8.90E+01 | 1.26E+01 | \(-\) 4.76E+01 | 2.54E+01 | |
F7 (F19 in CEC05) | SMPSO-RS | 9.55E+02 | 1.09E+03 | 1.01E+03 | 3.67E+01 |
SMPSO-AS | 9.68E+02 | 1.10E+03 | 1.03E+03 | 3.81E+01 | |
SMPSO-FS1 | 1.00E+03 | 1.23E+03 | 1.11E+03 | 5.95E+01 | |
SMPSO-FS2 | 1.01E+03 | 1.22E+03 | 1.13E+03 | 5.04E+01 | |
VSMPSO | 9.26E+02 | 9.97E+02 | 9.43E+02(+) | 1.51E+01 |
Function | Algorithm | Best | Worst | Mean (Friedman test) | SD |
---|---|---|---|---|---|
F1: Ellipsoid | SMPSO-RS | 2.29E+01 | 3.46E+02 | 1.13E+02 | 7.43E+01 |
SMPSO-AS | 1.24E+01 | 2.98E+02 | 8.49E+01 | 6.20E+01 | |
SMPSO-FS1 | 1.49E+02 | 9.16E+02 | 3.34E+02 | 1.74E+02 | |
SMPSO-FS2 | 1.50E+02 | 1.01E+03 | 3.37E+02 | 1.79E+02 | |
VSMPSO | 3.79E+00 | 2.53E+01 | 1.19E+01(+) | 6.13E+00 | |
F2: Rosenbrock | SMPSO-RS | 2.17E+02 | 4.82E+02 | 3.25E+02 | 5.69E+01 |
SMPSO-AS | 2.27E+02 | 4.45E+02 | 3.31E+02 | 4.94E+01 | |
SMPSO-FS1 | 3.43E+02 | 1.82E+03 | 9.13E+02 | 3.84E+02 | |
SMPSO-FS2 | 3.34E+02 | 2.81E+03 | 1.05E+03 | 6.04E+02 | |
VSMPSO | 1.14E+02 | 2.75E+02 | 1.88E+02(+) | 3.04E+01 | |
F3: Ackley | SMPSO-RS | 9.13E+00 | 1.64E+01 | 1.35E+01 | 1.79E+00 |
SMPSO-AS | 5.63E+00 | 1.73E+01 | 1.29E+01 | 2.77E+00 | |
SMPSO-FS1 | 1.72E+01 | 2.04E+01 | 1.91E+01 | 6.51E \(-\)01 | |
SMPSO-FS2 | 1.71E+01 | 2.04E+01 | 1.89E+01 | 7.75E\(-\)01 | |
VSMPSO | 4.09E+00 | 2.00E+01 | 8.68E+00(+) | 6.36E+00 | |
F4: Griewank | SMPSO-RS | 1.07E+00 | 3.87E+01 | 4.00E+00 | 7.08E+00 |
SMPSO-AS | 1.14E+00 | 1.93E+01 | 4.25E+00 | 4.52E+00 | |
SMPSO-FS1 | 8.17E+00 | 1.15E+02 | 2.48E+01 | 2.28E+01 | |
SMPSO-FS2 | 8.25E+00 | 5.26E+01 | 2.22E+01 | 1.14E+01 | |
VSMPSO | 6.42E \(-\)01 | 9.84E \(-\)01 | 8.34E \(-\)01(+) | 7.38E \(-\)02 | |
F5: Rastrigin | SMPSO-RS | 1.32E+02 | 2.75E+02 | 2.09E+02 | 3.57E+01 |
SMPSO-AS | 1.20E+02 | 2.76E+02 | 1.92E+02(+) | 3.92E+01 | |
SMPSO-FS1 | 4.28E+02 | 6.32E+02 | 5.32E+02 | 4.54E+01 | |
SMPSO-FS2 | 4.79E+02 | 6.22E+02 | 5.41E+02 | 3.94E+01 | |
VSMPSO | 2.50E+02 | 4.81E+02 | 4.04E+02 | 5.97E+01 | |
F6 (F10 in CEC05) | SMPSO-RS | \(-\) 1.96E+02 | \(-\) 3.90E+01 | \(-\) 1.23E+02(+) | 4.42E+01 |
SMPSO-AS | \(-\) 2.11E+02 | \(-\) 4.39E+00 | \(-\) 1.10E+02 | 5.26E+01 | |
SMPSO-FS1 | 1.89E+02 | 3.68E+02 | 2.80E+02 | 4.28E+01 | |
SMPSO-FS2 | 1.90E+02 | 3.63E+02 | 2.67E+02 | 4.82E+01 | |
VSMPSO | \(-\) 1.15E+01 | 1.87E+02 | 1.05E+02 | 5.72E+01 | |
F7 (F19 in CEC05) | SMPSO-RS | 1.02E+03 | 1.15E+03 | 1.08E+03 | 3.69E+01 |
SMPSO-AS | 1.05E+03 | 1.23E+03 | 1.10E+03 | 3.97E+01 | |
SMPSO-FS1 | 1.09E+03 | 1.34E+03 | 1.19E+03 | 6.13E+01 | |
SMPSO-FS2 | 1.07E+03 | 1.25E+03 | 1.17E+03 | 4.07E+01 | |
VSMPSO | 9.49E+02 | 1.04E+03 | 9.81E+02(+) | 2.49E+01 |
Fitness/time | Dimension | VSMPSO | SMPSO-RS | SMPSO-AS | SMPSO-FS1 | SMPSO-FS2 |
---|---|---|---|---|---|---|
F1: Ellipsoid | 30D | 2.33E+00/5.45E+01 | 8.84E+00/6.78E+00 | 4.21E+00/8.12E+00 | 4.77E+01/8.12E+00 | 3.68E+01/5.60E+00 |
50D | 1.19E+01/1.72E+02 | 1.13E+02/2.52E+01 | 8.49E+01/2.73E+01 | 3.34E+02/2.61E+01 | 3.37E+02/2.31E+01 | |
100D | 3.60E+01/8.71E+02 | 7.69E+01/6.08E+02 | 7.31E+01/2.57E+02 | 4.13E+02/6.06E+02 | 3.52E+02/1.87E+02 | |
F2: Rosenbrock | 30D | 1.12E+02/5.43E+01 | 1.52E+02/6.86E+00 | 1.38E+02/8.28E+00 | 3.01E+02/6.72E+00 | 2.62E+02/5.85E+00 |
50D | 1.88E+02/1.61E+02 | 3.25E+02/2.50E+01 | 3.31E+02/3.07E+01 | 9.13E+02/2.05E+01 | 1.05E+03/2.03E+01 | |
100D | 1.59E+02/8.24E+02 | 1.88E+02/6.07E+02 | 1.60E+02/2.54E+02 | 4.69E+02/5.76E+02 | 4.06E+02/2.00E+02 | |
F3: Ackley | 30D | 4.03E+00/5.52E+01 | 5.43E+00/6.95E+00 | 6.07E+00/8.16E+00 | 1.49E+01/5.90E+00 | 1.51E+01/5.76E+00 |
50D | 8.68E+00/1.81E+02 | 1.35E+01/5.76E+00 | 1.29E+01/3.12E+01 | 1.91E+01/3.12E+01 | 1.89E+01/2.56E+01 | |
100D | 1.06E+01/8.33E+02 | 1.41E+01/6.21E+02 | 1.50E+01/2.74E+02 | 1.65E+01/5.98E+02 | 1.67E+01/2.06E+02 | |
F4: Griewank | 30D | 8.54E\(-\)01/5.64E+01 | 7.98E\(-\)01/9.30E+00 | 4.98E\(-\)01/1.09E+01 | 3.26E+00/8.83E+00 | 3.33E+00/1.00E+01 |
50D | 8.34E\(-\)01/1.80E+02 | 4.00E+00/3.03E+01 | 4.25E+00/3.21E+01 | 2.48E+01/3.17E+01 | 2.22E+01/3.02E+01 | |
100D | 8.17E\(-\)01/8.49E+02 | 1.93E+00/6.23E+02 | 1.87E+00/2.75E+02 | 5.74E+00/6.22E+02 | 6.11E+00/2.03E+02 | |
F5: Rastingin | 30D | 9.92E+01/5.52E+01 | 2.51E+02/6.90E+00 | 8.80E+01/8.13E+00 | 2.95E+02/5.51E+00 | 2.95E+02/5.50E+00 |
50D | 2.09E+02/1.74E+02 | 2.50E+02/2.50E+01 | 1.92E+02/3.18E+01 | 5.32E+02/2.60E+01 | 5.41E+02/2.32E+01 | |
100D | 3.43E+02/8.80E+02 | 4.79E+02/6.08E+02 | 2.79E+02/2.52E+02 | 8.86E+02/5.97E+02 | 8.91E+02/1.86E+02 | |
F6 (F10 in CEC05) | 30D | \(-\) 2.09E+02/5.55E+01 | \(-\) 4.76E+01/5.85E+00 | \(-\) 2.18E+0/6.89E+00 | 6.03E+01/7.29E+00 | 4.99E+01/5.99E+00 |
50D | 1.05E+02/1.76E+02 | \(-\) 1.23E+02/2.22E+01 | \(-\) 1.10E+0/2.73E+01 | 2.80E+02/2.66E+01 | 2.67E+02/2.11E+01 | |
100D | 7.28E+02/9.45E+02 | 9.40E+02/7.16E+02 | 1.32E+03/2.92E+02 | 1.21E+03/6.57E+02 | 1.14E+03/2.38E+02 | |
F7 (F19 in CEC05) | 30D | 1.01E+03/5.58E+01 | 9.43E+02/6.28E+00 | 1.03E+03/7.73E+00 | 1.11E+03/8.12E+00 | 1.13E+03/6.79E+00 |
50D | 9.81E+02/1.77E+02 | 1.08E+03/2.41E+01 | 1.10E+03/2.90E+01 | 1.19E+03/2.81E+01 | 1.17E+03/2.21E+01 | |
100D | 1.40E+03/1.11E+03 | 1.41E+03/1.08E+03 | 1.46E+03/4.70E+02 | 1.46E+03/1.00E+03 | 1.45E+03/4.01E+02 | |
All/NDS/DS | 30D | 7/4/3 | 7/7/0 | 7/5/2 | 7/4/3 | 7/4/3 |
50D | 7/5/2 | 7/7/0 | 7/3/4 | 7/2/5 | 7/7/0 | |
100D | 7/6/1 | 7/3/4 | 7/5/2 | 7/0/7 | 7/7/0 |
Function | Algorithm | Best | Worst | Mean | SD |
---|---|---|---|---|---|
F1: Ellipsoid | SMPSO-RS | 3.04E+01 | 1.33E+02 | 7.69E+01 | 2.70E+01 |
SMPSO-AS | 2.65E+01 | 1.37E+02 | 7.31E+01 | 2.59E+01 | |
SMPSO-FS1 | 1.68E+02 | 9.51E+02 | 4.13E+02 | 2.04E+02 | |
SMPSO-FS2 | 1.75E+02 | 6.29E+02 | 3.52E+02 | 9.56E+01 | |
VSMPSO |
2.17E+01
|
6.20E+01
| 3.60E+01(+) |
9.31E+00
| |
F2: Rosenbrock | SMPSO-RS | 1.53E+02 | 2.40E+02 | 1.88E+02 | 2.07E+01 |
SMPSO-AS |
1.30E+02
| 2.19E+02 | 1.60E+02 | 1.71E+01 | |
SMPSO-FS1 | 2.62E+02 | 1.25E+03 | 4.69E+02 | 1.90E+02 | |
SMPSO-FS2 | 2.67E+02 | 6.40E+02 | 4.06E+02 | 6.48E+01 | |
VSMPSO | 1.31E+02 |
2.09E+02
| 1.59E+02(+) |
1.54E+01
| |
F3: Ackley | SMPSO-RS | 1.21E+01 | 1.56E+01 | 1.41E+01 | 8.14E\(-\)01 |
SMPSO-AS | 1.34E+01 | 1.58E+01 | 1.50E+01 | 5.31E\(-\)01 | |
SMPSO-FS1 | 1.55E+01 | 1.77E+01 | 1.65E+01 | 6.04E\(-\)01 | |
SMPSO-FS2 | 1.42E+01 | 1.83E+01 | 1.67E+01 | 8.70E\(-\)01 | |
VSMPSO |
8.24E+00
|
1.25E+01
| 1.06E+01(+) |
8.99E
\(-\)
01
| |
F4: Griewank | SMPSO-RS | 1.24E+00 | 3.10E+00 | 1.93E+00 | 5.01E\(-\)01 |
SMPSO-AS | 1.29E+00 | 3.65E+00 | 1.87E+00 | 5.54E\(-\)01 | |
SMPSO-FS1 | 3.45E+00 | 9.26E+00 | 5.74E+00 | 1.62E+00 | |
SMPSO-FS2 | 3.34E+00 | 1.07E+01 | 6.11E+00 | 1.80E+00 | |
VSMPSO |
6.58E
\(-\)
01
|
1.01E+00
| 8.17E \(-\)01(+) |
8.24E
\(-\)
02
| |
F5: Rastrigin | SMPSO-RS | 2.79E+02 | 4.29E+02 | 3.43E+02 | 5.20E+01 |
SMPSO-AS |
2.06E+02
|
3.70E+02
| 2.79E+02(+) |
4.07E+01
| |
SMPSO-FS1 | 8.29E+02 | 9.49E+02 | 8.86E+02 | 3.17E+01 | |
SMPSO-FS2 | 8.26E+02 | 9.91E+02 | 8.91E+02 | 3.77E+01 | |
VSMPSO | 3.09E+02 | 7.32E+02 | 4.79E+02 | 8.71E+01 | |
F6 (F10 in CEC05) | SMPSO-RS | 7.54E+02 | 1.36E+03 | 9.40E+02 | 1.24E+02 |
SMPSO-AS | 8.47E+02 | 2.68E+03 | 1.32E+03 | 4.95E+02 | |
SMPSO-FS1 | 8.54E+02 | 1.63E+03 | 1.21E+03 | 2.00E+02 | |
SMPSO-FS2 | 8.05E+02 | 1.73E+03 | 1.14E+03 | 2.06E+02 | |
VSMPSO |
5.86E+02
|
8.36E+02
| 7.28E+02(+) |
6.55E+01
| |
F7 (F19 in CEC05) | SMPSO-RS | 1.35E+03 | 1.47E+03 | 1.41E+03 | 3.13E+01 |
SMPSO-AS | 1.37E+03 | 1.54E+03 | 1.46E+03 | 4.14E+01 | |
SMPSO-FS1 | 1.36E+03 | 1.57E+03 | 1.46E+03 | 4.80E+01 | |
SMPSO-FS2 | 1.38E+03 | 1.53E+03 | 1.45E+03 | 4.26E+01 | |
VSMPSO |
1.33E+03
|
1.46E+03
| 1.40E+03(+) |
4.05E+01
|
Parameter sensitivity analysis
Function | Algorithm | Best | Worst | Mean (Friedman test) | SD | Meantime |
---|---|---|---|---|---|---|
F1: Ellipsoid | VSMPSO-50 | 2.20E+00 | 9.09E+00 | 5.60E+00 | 2.41E+00 | 5.61E+01 |
VSMPSO-60 | 1.60E+00 | 5.17E+00 | 4.48E+00 | 1.40E+00 | 6.30E+01 | |
VSMPSO-70 | 1.71E+00 | 3.63E+00 | 3.17E+00 | 7.46E\(-\)01 | 6.99E+01 | |
VSMPSO-80 | 4.45E \(-\)01 | 1.41E+00 | 7.69E \(-\)01(+) | 4.65E \(-\)01 | 7.64E+01 | |
VSMPSO-90 | 7.38E\(-\)01 | 2.89E+00 | 2.43E+00 | 7.21E\(-\)01 | 8.32E+01 | |
VSMPSO-100 | 5.41E\(-\)01 | 3.55E+00 | 1.56E+00 | 1.37E+00 | 8.93E+01 | |
F2: Rosenbrock | SLPSO-50 | 1.16E+02 | 1.72E+02 | 1.47E+02 | 2.20E+01 | 6.24E+01 |
VSMPSO-60 | 6.69E+01 | 1.78E+02 | 9.75E+01(+) | 2.90E+01 | 7.10E+01 | |
VSMPSO-70 | 8.89E+01 | 1.22E+02 | 1.12E+02 | 1.35E+01 | 7.55E+01 | |
VSMPSO-80 | 1.03E+02 | 1.27E+02 | 1.14E+02 | 7.61E+00 | 8.23E+01 | |
VSMPSO-90 | 8.41E+01 | 1.40E+02 | 1.22E+02 | 1.63E+01 | 8.91E+01 | |
VSMPSO-100 | 7.17E+01 | 1.26E+02 | 1.11E+02 | 2.26E+01 | 9.56E+01 | |
F3: Ackley | SLPSO-50 | 7.47E+00 | 2.00E+01 | 1.87E+01 | 3.81E+00 | 5.72E+01 |
VSMPSO-60 | 4.82E+00 | 2.00E+01 | 7.86E+00 | 6.16E+00 | 6.37E+01 | |
VSMPSO-70 | 4.58E+00 | 4.85E+00 | 4.60E+00 | 6.72E\(-\)02 | 7.02E+01 | |
VSMPSO-80 | 4.01E+00 | 4.09E+00 | 4.02E+00 | 1.87E \(-\)02 | 7.69E+01 | |
VSMPSO-90 | 3.62E+00 | 3.82E+00 | 3.63E+00(+) | 5.10E\(-\)02 | 8.37E+01 | |
VSMPSO-100 | 3.93E+00 | 5.17E+00 | 4.57E+00 | 3.82E\(-\)01 | 9.03E+01 | |
F4: Griewank | SLPSO-50 | 9.50E\(-\)01 | 9.81E\(-\)01 | 9.59E\(-\)01 | 1.40E \(-\)02 | 5.70E+01 |
VSMPSO-60 | 8.61E\(-\)01 | 9.66E\(-\)01 | 9.20E\(-\)01 | 5.30E\(-\)02 | 6.33E+01 | |
VSMPSO-70 | 8.38E\(-\)01 | 9.81E\(-\)01 | 9.21E\(-\)01 | 7.02E\(-\)02 | 7.05E+01 | |
VSMPSO-80 | 8.05E\(-\)01 | 8.55E\(-\)01 | 8.21E\(-\)01 | 1.76E\(-\)02 | 7.78E+01 | |
VSMPSO-90 | 7.13E\(-\)01 | 8.05E \(-\)01 | 7.99E\(-\)01 | 2.34E\(-\)02 | 8.37E+01 | |
VSMPSO-100 | 4.99E \(-\)01 | 8.40E\(-\)01 | 7.19E \(-\)01(+) | 1.47E\(-\)01 | 9.02E+01 | |
F5: Rastrigin | SLPSO-50 | 2.27E+02 | 2.69E+02 | 2.37E+02 | 1.81E+01 | 5.69E+01 |
VSMPSO-60 | 2.33E+02 | 2.62E+02 | 2.50E+02 | 1.32E+01 | 6.41E+01 | |
VSMPSO-70 | 2.27E+02 | 2.84E+02 | 2.64E+02 | 1.92E+01 | 7.05E+01 | |
VSMPSO-80 | 2.42E+02 | 2.80E+02 | 2.58E+02 | 1.83E+01 | 7.76E+01 | |
VSMPSO-90 | 1.56E+02 | 2.52E+02 | 1.83E+02 | 4.00E+01 | 8.39E+01 | |
VSMPSO-100 | 1.22E+02 | 1.58E+02 | 1.46E+02(+) | 1.61E+01 | 9.04E+01 | |
F6 (F10 in CEC05) | SLPSO-50 | \(-\) 1.07E+02 | \(-\) 1.72E+01 | \(-\) 6.13E+01 | 2.08E+01 | 6.36E+01 |
VSMPSO-60 | \(-\) 9.76E+01 | \(-\) 1.90E+01 | \(-\) 6.07E+01 | 2.39E+01 | 7.09E+01 | |
VSMPSO-70 | \(-\) 8.73E+01 | \(-\) 6.43E+00 | \(-\) 5.89E+01 | 2.22E+01 | 7.71E+01 | |
VSMPSO-80 | \(-\) 9.72E+01 | \(-\) 1.79E+01 | \(-\) 5.81E+01 | 2.26E+01 | 8.61E+01 | |
VSMPSO-90 | \(-\) 1.14E+02 | 2.63E+01 | \(-\) 4.48E+01 | 3.26E+01 | 9.13E+01 | |
VSMPSO-100 | \(-\) 1.87E+02 | \(-\) 1.66E+01 | \(-\) 1.06E+02(+) | 4.96E+01 | 9.74E+01 | |
F7 (F19 in CEC05) | SLPSO-50 | 9.32E+02 | 9.51E+02 | 9.44E+02 | 8.89E+00 | 6.11E+01 |
VSMPSO-60 | 9.23E+02 | 1.01E+03 | 9.45E+02 | 1.90E+01 | 7.26E+01 | |
VSMPSO-70 | 9.23E+02 | 9.39E+02 | 9.37E+02(+) | 6.17E+00 | 7.52E+01 | |
VSMPSO-80 | 9.23E+02 | 9.77E+02 | 9.40E+02 (\(\approx \)) | 1.37E+01 | 8.04E+01 | |
VSMPSO-90 | 9.31E+02 | 9.50E+02 | 9.47E+02 | 6.07E+00 | 8.90E+01 | |
VSMPSO-100 | 9.38E+02 | 9.58E+02 | 9.42E+02 | 7.22E+00 | 9.30E+01 |
Function | Algorithm | Best | Worst | Mean | SD | Meantime |
---|---|---|---|---|---|---|
F1: Ellipsoid | VSMPSO-50 | 8.61E+00 | 9.35E+00 | 8.96E+00(+) | 1.97E \(-\)01 | 1.63E+02 |
VSMPSO-60 | 3.67E+00 | 2.14E+01 | 1.11E+01 | 3.73E+00 | 1.87E+02 | |
VSMPSO-70 | 4.56E+00 | 2.68E+01 | 1.16E+01 | 5.41E+00 | 2.10E+02 | |
VSMPSO-80 | 3.26E+00 | 3.43E+01 | 1.19E+01 | 7.18E+00 | 2.33E+02 | |
VSMPSO-90 | 3.41E+00 | 2.54E+01 | 1.06E+01 | 4.92E+00 | 2.56E+02 | |
VSMPSO-100 | 2.36E+00 | 2.62E+01 | 1.04E+01 | 6.38E+00 | 2.83E+02 | |
F2: Rosenbrock | SLPSO-50 | 8.78E+01 | 1.74E+02 | 1.33E+02(+) | 1.91E+01 | 1.71E+02 |
VSMPSO-60 | 9.78E+01 | 1.72E+02 | 1.41E+02 | 1.97E+01 | 1.94E+02 | |
VSMPSO-70 | 1.33E+02 | 2.32E+02 | 1.70E+02 | 2.59E+01 | 2.16E+02 | |
VSMPSO-80 | 1.51E+02 | 2.74E+02 | 2.03E+02 | 3.33E+01 | 2.40E+02 | |
VSMPSO-90 | 1.24E+02 | 2.93E+02 | 1.95E+02 | 3.74E+01 | 2.66E+02 | |
VSMPSO-100 | 1.26E+02 | 2.30E+02 | 1.62E+02 | 3.00E+01 | 2.86E+02 | |
F3: Ackley | SLPSO-50 | 1.99E+01 | 2.00E+01 | 2.00E+01 | 5.91E\(-\)03 | 1.68E+02 |
VSMPSO-60 | 1.90E+01 | 2.00E+01 | 1.99E+01 | 1.71E \(-\)01 | 1.90E+02 | |
VSMPSO-70 | 4.43E+00 | 2.00E+01 | 1.59E+01 | 6.35E+00 | 2.15E+02 | |
VSMPSO-80 | 4.05E+00 | 6.44E+00 | 4.58E+00(+) | 6.82E\(-\)01 | 2.34E+02 | |
VSMPSO-90 | 3.84E+00 | 6.10E+00 | 4.96E+00 | 7.12E\(-\)01 | 2.63E+02 | |
VSMPSO-100 | 3.74E+00 | 6.82E+00 | 5.31E+00 | 7.60E\(-\)01 | 2.86E+02 | |
F4: Griewank | SLPSO-50 | 8.04E\(-\)01 | 1.02E+00 | 9.02E\(-\)01 | 4.69E \(-\)02 | 1.66E+02 |
VSMPSO-60 | 8.00E\(-\)01 | 9.91E\(-\)01 | 9.02E\(-\)01 | 4.96E\(-\)02 | 1.90E+02 | |
VSMPSO-70 | 7.39E\(-\)01 | 1.01E+00 | 8.64E\(-\)01 | 6.02E\(-\)02 | 2.13E+02 | |
VSMPSO-80 | 6.42E\(-\)01 | 1.02E+00 | 8.24E\(-\)01 | 9.82E\(-\)02 | 2.35E+02 | |
VSMPSO-90 | 6.05E\(-\)01 | 9.19E \(-\)01 | 7.41E\(-\)01 | 6.39E\(-\)02 | 2.62E+02 | |
VSMPSO-100 | 5.32E \(-\)01 | 9.73E\(-\)01 | 6.90E \(-\)01(+) | 1.21E\(-\)01 | 2.87E+02 | |
F5: Rastrigin | SLPSO-50 | 3.86E+02 | 5.07E+02 | 4.54E+02 | 3.25E+01 | 1.73E+02 |
VSMPSO-60 | 3.89E+02 | 5.05E+02 | 4.50E+02 | 2.94E+01 | 1.96E+02 | |
VSMPSO-70 | 3.60E+02 | 4.91E+02 | 4.28E+02 | 3.59E+01 | 2.21E+02 | |
VSMPSO-80 | 2.80E+02 | 5.31E+02 | 3.88E+02 | 7.04E+01 | 2.42E+02 | |
VSMPSO-90 | 1.87E+02 | 4.33E+02 | 3.12E+02 | 6.34E+01 | 2.65E+02 | |
VSMPSO-100 | 1.04E+02 | 3.01E+02 | 1.77E+02(+) | 4.41E+01 | 2.92E+02 | |
F6 (F10 in CEC05) | SLPSO-50 | 8.72E+01 | 2.01E+02 | 1.36E+02 | 2.88E+01 | 1.74E+02 |
VSMPSO-60 | 9.48E+01 | 2.16E+02 | 1.50E+02 | 2.73E+01 | 2.00E+02 | |
VSMPSO-70 | 8.00E+01 | 1.94E+02 | 1.37E+02 | 2.74E+01 | 2.20E+02 | |
VSMPSO-80 | 7.28E+01 | 2.29E+02 | 1.57E+02 | 4.41E+01 | 2.40E+02 | |
VSMPSO-90 | \(-\) 6.06E+01 | 1.99E+02 | 1.10E+02 | 5.68E+01 | 2.66E+02 | |
SLPSO-100 | \(-\) 9.42E+01 | 7.01E+01 | \(-\) 4.33E+01(+) | 4.72E+01 | 2.89E+02 | |
F7 (F19 in CEC05) | SLPSO-50 | 9.71E+02 | 9.94E+02 | 9.82E+02 | 1.15E+01 | 1.73E+02 |
VSMPSO-60 | 9.56E+02 | 1.04E+03 | 9.84E+02 | 2.22E+01 | 1.96E+02 | |
VSMPSO-70 | 9.58E+02 | 1.03E+03 | 9.89E+02 | 2.06E+01 | 2.19E+02 | |
VSMPSO-80 | 9.73E+02 | 9.93E+02 | 9.75E+02 | 3.52E+00 | 2.39E+02 | |
VSMPSO-90 | 9.54E+02 | 9.79E+02 | 9.66E+02(+) | 9.52E+00 | 2.64E+02 | |
VSMPSO-100 | 9.53E+02 | 1.05E+03 | 9.75E+02 | 2.73E+01 | 2.88E+02 |
Function | Algorithm | Best | Worst | Mean | SD | Meantime |
---|---|---|---|---|---|---|
F1: Ellipsoid | VSMPSO-50 | 4.02E+01 | 6.96E+01 | 5.60E+01 | 7.63E+00 | 7.30E+02 |
VSMPSO-60 | 2.86E+01 | 8.16E+01 | 4.53E+01 | 9.55E+00 | 8.50E+02 | |
VSMPSO-70 | 2.95E+01 | 4.32E+01 | 4.18E+01 | 2.43E+00 | 9.76E+02 | |
VSMPSO-80 | 2.03E+01 | 5.68E+01 | 3.43E+01 | 1.00E+01 | 1.10E+03 | |
VSMPSO-90 | 2.19E+01 | 4.58E+01 | 3.40E+01 | 6.86E+00 | 1.23E+03 | |
VSMPSO-100 | 1.87E+01 | 3.91E+01 | 2.14E+01(+) | 3.79E+00 | 1.37E+03 | |
F2: Rosenbrock | VSMPSO-50 | 1.60E+02 | 2.22E+02 | 1.89E+02 | 1.81E+01 | 7.39E+02 |
VSMPSO-60 | 1.56E+02 | 1.99E+02 | 1.80E+02 | 1.18E+01 | 8.59E+02 | |
VSMPSO-70 | 1.64E+02 | 2.01E+02 | 1.79E+02 | 6.45E+00 | 9.88E+02 | |
VSMPSO-80 | 1.48E+02 | 1.86E+02 | 1.67E+02 | 1.41E+01 | 1.11E+03 | |
VSMPSO-90 | 1.28E+02 | 1.70E+02 | 1.47E+02 | 1.24E+01 | 1.24E+03 | |
VSMPSO-100 | 1.15E+02 | 1.44E+02 | 1.31E+02(+) | 8.27E+00 | 1.38E+03 | |
F3: Ackley | VSMPSO-50 | 1.40E+01 | 1.74E+01 | 1.61E+01 | 6.52E\(-\)01 | 7.40E+02 |
VSMPSO-60 | 1.10E+01 | 1.39E+01 | 1.27E+01 | 9.35E\(-\)01 | 8.53E+02 | |
VSMPSO-70 | 1.23E+01 | 1.37E+01 | 1.25E+01 | 4.28E \(-\)01 | 9.86E+02 | |
VSMPSO-80 | 8.77E+00 | 1.24E+01 | 1.02E+01(\(\approx \)) | 7.13E\(-\)01 | 1.11E+03 | |
VSMPSO-90 | 8.83E+00 | 1.06E+01 | 1.04E+01 | 4.81E\(-\)01 | 1.24E+03 | |
VSMPSO-100 | 8.27E+00 | 1.09E+01 | 9.77E+00(+) | 6.56E\(-\)01 | 1.37E+03 | |
F4: Griewank | VSMPSO-50 | 9.39E\(-\)01 | 1.08E+00 | 1.01E+00 | 4.30E\(-\)02 | 7.40E+02 |
VSMPSO-60 | 8.82E\(-\)01 | 1.04E+00 | 9.62E\(-\)01 | 5.17E\(-\)02 | 8.60E+02 | |
VSMPSO-70 | 8.41E\(-\)01 | 1.02E+00 | 9.46E\(-\)01 | 3.60E \(-\)02 | 9.87E+02 | |
VSMPSO-80 | 6.58E\(-\)01 | 1.01E+00 | 8.38E\(-\)01 | 8.18E\(-\)02 | 1.11E+03 | |
VSMPSO-90 | 5.67E\(-\)01 | 9.52E \(-\)01 | 7.57E\(-\)01 | 1.00E\(-\)01 | 1.24E+03 | |
VSMPSO-100 | 4.22E \(-\)01 | 9.81E\(-\)01 | 6.56E \(-\)01(+) | 1.17E\(-\)01 | 1.38E+03 | |
F5: Rastrigin | VSMPSO-50 | 7.50E+02 | 9.83E+02 | 8.71E+02 | 7.05E+01 | 7.35E+02 |
VSMPSO-60 | 7.10E+02 | 8.40E+02 | 7.82E+02 | 5.27E+01 | 8.52E+02 | |
VSMPSO-70 | 5.67E+02 | 6.30E+02 | 5.83E+02 | 2.39E+01 | 9.83E+02 | |
VSMPSO-80 | 3.98E+02 | 7.18E+02 | 5.31E+02 | 7.42E+01 | 1.11E+03 | |
VSMPSO-90 | 2.98E+02 | 4.91E+02 | 4.05E+02 | 5.08E+01 | 1.23E+03 | |
VSMPSO-100 | 1.75E+02 | 4.32E+02 | 2.32E+02(+) | 5.21E+01 | 1.36E+03 | |
F6 (F10 in CEC05) | VSMPSO-50 | 6.32E+02 | 7.26E+02 | 6.87E+02 | 3.40E+01 | 9.01E+02 |
VSMPSO-60 | 6.21E+02 | 7.38E+02 | 6.69E+02(+) | 3.97E+01 | 8.99E+02 | |
VSMPSO-70 | 6.35E+02 | 7.63E+02 | 6.96E+02 | 3.60E+01 | 1.03E+03 | |
VSMPSO-80 | 6.03E+02 | 7.72E+02 | 7.00E+02 | 4.31E+01 | 1.14E+03 | |
VSMPSO-90 | 6.67E+02 | 8.44E+02 | 7.44E+02 | 6.43E+01 | 1.28E+03 | |
VSMPSO-100 | 6.34E+02 | 2.50E+03 | 8.49E+02 | 3.52E+02 | 1.40E+03 | |
F7 (F19 in CEC05) | VSMPSO-50 | 1.34E+03 | 1.38E+03 | 1.36E+03(+) | 1.16E+01 | 1.22E+03 |
VSMPSO-60 | 1.36E+03 | 1.41E+03 | 1.37E+03 (\(\approx \)) | 8.52E+00 | 1.21E+03 | |
VSMPSO-70 | 1.35E+03 | 1.36E+03 | 1.36E+03 (\(\approx \)) | 2.54E+00 | 1.33E+03 | |
VSMPSO-80 | 1.32E+03 | 1.46E+03 | 1.39E+03(\(\approx \)) | 3.58E+01 | 1.45E+03 | |
VSMPSO-90 | 1.33E+03 | 1.46E+03 | 1.37E+03 (\(\approx \)) | 4.69E+01 | 1.58E+03 | |
VSMPSO-100 | 1.33E+03 | 1.43E+03 | 1.39E+03 (\(\approx \)) | 1.66E+01 | 1.71E+03 |
Function | Dimension | VSMPSO-50 | VSMPSO-60 | VSMPSO-70 | VSMPSO-80 | VSMPSO-90 | VSMPSO-100 |
---|---|---|---|---|---|---|---|
F1 (Ellipsoid) | 30D | 5.60E+00/5.61E+01 | 4.48E+00/6.30E+01 | 3.17E+00/6.99E+01 | 7.69E\(-\)01/7.64E+01 | 2.43E+00/8.32E+01 | 1.56E+00/8.93E+01 |
50D | 8.96E+00/1.63E+02 | 1.11E+01/1.87E+02 | 1.16E+01/2.10E+02 | 1.19E+01/2.33E+02 | 1.06E+01/2.56E+02 | 1.04E+01/2.83E+02 | |
100D | 5.60E+01/7.30E+02 | 4.53E+01/8.50E+02 | 4.18E+01/9.76E+02 | 3.43E+01/1.10E+03 | 3.40E+01/1.23E+03 | 2.14E+01/1.37E+03 | |
F2 (Rosenbrock) | 30D | 1.47E+02/6.24E+01 | 9.75E+01/7.10E+01 | 1.12E+02/7.55E+01 | 1.14E+02/8.23E+01 | 1.22E+02/8.91E+01 | 1.11E+02/9.56E+01 |
50D | 1.33E+02/1.71E+02 | 1.41E+02/1.94E+02 | 1.70E+02/2.16E+02 | 2.03E+02/2.40E+02 | 1.95E+02/2.66E+02 | 1.62E+02/2.86E+02 | |
100D | 1.89E+02/7.39E+02 | 1.80E+02/8.59E+02 | 1.79E+02/9.88E+02 | 1.67E+02/1.11E+03 | 1.47E+02/1.24E+03 | 1.31E+02/1.38E+03 | |
F3 (Ackley) | 30D | 1.87E+01/5.72E+01 | 7.86E+00/6.37E+01 | 4.60E+00/7.02E+01 | 4.02E+00/7.69E+01 | 3.63E+00/8.37E+01 | 4.57E+00/9.03E+01 |
50D | 2.00E+01/1.68E+02 | 1.99E+01/1.90E+02 | 1.59E+01/2.15E+02 | 4.58E+00/2.34E+02 | 4.96E+00/2.63E+02 | 5.31E+00/2.86E+02 | |
100D | 1.61E+01/7.40E+02 | 1.27E+01/8.53E+02 | 1.25E+01/9.86E+02 | 1.02E+01/1.11E+03 | 1.04E+01/1.24E+03 | 9.77E+00/1.37E+03 | |
F4 (Griewank) | 30D | 9.59E\(-\)01/5.70E+01 | 9.20E\(-\)01/6.33E+01 | 9.21E\(-\)01/7.05E+01 | 8.21E\(-\)01/7.78+01 | 7.99E\(-\)01/8.37E+01 | 7.19E\(-\)01/9.02E+01 |
50D | 9.02E\(-\)01/1.66E+02 | 9.02E\(-\)01/1.90E+02 | 8.64E\(-\)01/2.13E+02 | 8.24E\(-\)01/2.35E+02 | 7.41E\(-\)01/2.62E+02 | 6.90E\(-\)01/2.87E+02 | |
100D | 1.01E+00/7.40E+02 | 9.62E\(-\)01/8.60E+02 | 9.46E\(-\)01/9.87E+02 | 8.38E\(-\)01/1.11E+03 | 7.57E\(-\)01/1.24E+03 | 6.56E\(-\)01/1.38E+03 | |
F5 (Rastrigin) | 30D | 2.37E+02/5.69E+01 | 2.50E+02/6.41E+01 | 2.64E+02/7.05E+01 | 2.58E+02/7.76E+01 | 1.83E+02/8.39E+01 | 1.46E+02/9.04E+01 |
50D | 4.54E+02/1.73E+02 | 4.50E+02/1.96E+02 | 4.28E+02/2.21E+02 | 3.88E+02/2.42E+02 | 3.12E+02/2.65E+02 | 1.77E+02/2.92E+02 | |
100D | 8.71E+02/7.35E+02 | 7.82E+02/8.52E+02 | 5.83E+02/9.83E+02 | 5.31E+02/1.11E+03 | 4.05E+02/1.23E+03 | 2.32E+02/1.36E+03 | |
F6 (F10 in CEC05) | 30D | \(-\) 6.13E+01/6.36E+01 | \(-\) 6.07E+01/7.09E+01 | \(-\) 5.89E+01/7.71E+01 | \(-\) 5.81E+01/8.61E+01 | \(-\) 4.48E+01/9.13E+01 | \(-\) 1.06E+02/9.74E+01 |
50D | 1.36E+02/1.74E+02 | 1.50E+02/2.00E+02 | 1.37E+02/2.20E+02 | 1.57E+02/2.40E+02 | 1.10E+02/2.66E+02 | \(-\) 4.33E+01/2.89E+02 | |
100D | 6.87E+02/9.01E+02 | 6.69E+02/8.99E+02 | 6.96E+02/1.03E+03 | 7.00E+02/1.14E+03 | 7.44E+02/1.28E+03 | 8.49E+02/1.40E+03 | |
F7 (F19 in CEC05) | 30D | 9.44E+02/6.11E+01 | 9.45E+02/7.26E+01 | 9.37E+02/7.52E+01 | 9.40E+02/8.04E+01 | 9.47E+02/8.90E+01 | 9.42E+02/9.30E+01 |
50D | 9.82E+02/1.73E+02 | 9.84E+02/1.96E+02 | 9.89E+02/2.19E+02 | 9.75E+02/2.39E+02 | 9.66E+02/2.64E+02 | 9.75E+02/2.88E+02 | |
100D | 1.36E+03/1.22E+03 | 1.37E+03/1.21E+03 | 1.36E+03/1.33E+03 | 1.39E+03/1.45E+03 | 1.37E+03/1.58E+03 | 1.39E+03/1.71E+03 | |
All/NDS/DS | 30D | 7/7/0 | 7/4/3 | 7/3/4 |
7/3/4
| 7/3/4 | 7/3/4 |
50D | 7/7/0 | 7/3/4 | 7/3/4 |
7/4/3
| 7/4/3 | 7/3/4 | |
100D | 7/6/1 | 7/7/0 | 7/6/1 |
7/5/2
| 7/4/3 | 7/5/2 |
Mean/time | Dimension | VSMPSO-CEC17 | SAHO-CEC17 |
---|---|---|---|
F8 | 50D | 4.01E+03/2.38E+02 | 3.25E+03/2.47E+04 |
100D | 5.43E+03/1.10E+03 | 3.89E+03/2.67E+04 | |
F9 | 50D | 9.53E+03/2.38E+02 | 7.01E+03/6.55E+03 |
100D | 1.76E+04/1.11E+03 | 1.28E+04/3.01E+04 | |
F10 | 50D | 3.94E+03/2.39E+02 | 3.69E+03/6.02E+03 |
100D | 3.99E+03/1.11E+03 | 3.84E+03/3.37E+04 | |
F11 | 50D | 5.76E+03/2.39E+02 | 4.06E+03/5.34E+03 |
100D | 7.54E+03/1.11E+03 | 5.03E+03/2.39E+04 | |
All/NDS/DS | 50D | 7/7/0 | 7/7/0 |